Phase space properties of cosmological models in f(Q, T) gravity

Abstract The Weyl type f ( Q , T ) gravity is the modification of f ( Q ) gravity and f ( Q , T ) theories, where non-metricity is denoted by Q and T is the trace of the energy–momentum tensor. Together with a geometric explanation for dark energy, the theory can provide an exact interpretation of the transformation of the late-time Universe and the observable data. In this study, we present an accelerated cosmic model of the Universe in f ( Q , T ) gravity. We consider the model of f ( Q , T ) gravity as, $$f(Q,T) = -Q+\phi (Q,T)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>f</mml:mi> <mml:mo>(</mml:mo> <mml:mi>Q</mml:mi> <mml:mo>,</mml:mo> <mml:mi>T</mml:mi> <mml:mo>)</mml:mo> <mml:mo>=</mml:mo> <mml:mo>-</mml:mo> <mml:mi>Q</mml:mi> <mml:mo>+</mml:mo> <mml:mi>ϕ</mml:mi> <mml:mo>(</mml:mo> <mml:mi>Q</mml:mi> <mml:mo>,</mml:mo> <mml:mi>T</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> . We examine the energy condition for the model of f ( Q , T ) gravity and find out that our model satisfies the null and strong energy conditions at the same time, it violates the weak and dominant energy conditions. After that, we perform the phase-space study of our cosmological model with and without interaction independently. In case of the absence of interaction, we get six critical points out of which three critical points are stable critical points while the rest three critical points are saddle. When we perform the stability analysis in the presence of interaction, we get three critical points out of which one critical point is stable while the rest two are saddle points. The phase-plot analysis also shows the cosmological models in f ( Q , T ) gravity.